Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in JAVA):

Solution:
import java.util.*;
public class ProblemC {
	
	public static StringBuilder sb;
    public static int[] R, C;
	public static void main (String[] argc)
	{
		Scanner sc = new Scanner(System.in);
		int n, m;
		n = sc.nextInt();
		m = sc.nextInt();
		int[][] target = new int[n+1][m+1];
		R = new int[n+1];
		C = new int[m+1];
		
		int s = 0;
		for(int i = 1; i<= n; i++)
		{
			for(int j = 1; j <= m; j++)
			{
				target[i][j] = sc.nextInt();
				s += target[i][j];
			}
		}
		
		sb = new StringBuilder();
		int cc, rr;
		if(n > m)
		{
			cc = doCols(target,C,n,m);
			rr = doRows(target,R, n, m);
		}
		else
		{
			rr = doRows(target, R, n,m);
			cc = doCols(target, C, n, m);
		}
		
		if( (cc*n + rr*m) != s) 
		{	
			sb.append("-1");
		}
		else
		{
			sb.append(cc+rr);
			sb.append("\n");
			for(int i = 1; i <= n; i++)
			{
				for(int j = 1; j <= R[i]; j++)
				{
					sb.append("row ");
					sb.append(i);
					sb.append("\n");
				}
			}
			
			for(int i = 1; i <= m; i++)
			{
				for(int j = 1; j <= C[i]; j++)
				{
					sb.append("col ");
					sb.append(i);
					sb.append("\n");
				}
			}
		}
		
		System.out.println(sb.toString());
	}
	
	
	public static int doRows(int[][] target, int[] R, int n, int m)
	{
		int ans = 0;
		for(int i = 1; i <= n; i++)
		{
			int min_V = 1000;
			for(int j = 1; j <= m; j++)
			{
				min_V = Math.min(min_V, target[i][j]);
			}
			R[i] = min_V;
			for(int j = 1; j <= m; j++)
			{
			    target[i][j] -= min_V;
			} 
			ans += min_V;
		}
		return ans;
		
	}
	
	public static int doCols(int[][] target, int[] C, int n, int m)
	{
		int ans = 0;
		for(int j = 1; j <= m; j++)
		{
			int min_V = 1000;
			for(int i = 1; i <= n ; i++)
			{
				min_V = Math.min(min_V, target[i][j]);
			}
			C[j] = min_V;
			for(int i = 1; i <= n; i++)
			{
			    target[i][j] -= min_V;
			}
			ans += min_V;
		}
		return ans;
	}

}